List-Decodable Folded Quantum Hermitian Codes
For quantum error correction, this provides a new family of codes with optimal list-decodability and improved alphabet size efficiency, though it is an incremental extension of existing folded quantum Reed-Solomon codes to Hermitian codes.
This paper constructs folded quantum Hermitian codes and proves they are list-decodable up to the quantum Singleton bound, matching the best possible trade-off between rate and error-correction radius. Compared to folded quantum Reed-Solomon codes, these codes achieve comparable lengths over smaller alphabets, enabling more efficient implementations.
Folded Reed-Solomon codes, introduced by Guruswami and Rudra in 2007, have been shown to achieve the information-theoretically best possible trade-off between the rate of a code and the error-correction radius. In 2024, Bergamaschi, Golowich and Gunn extended this framework by constructing folded quantum Reed-Solomon codes (CSS codes obtained by folding) demonstrating that these codes tolerate errors up to the quantum Singleton bound. In this paper, we construct folded quantum Hermitian codes using the CSS framework and show that these codes are also list-decodable, tolerating errors up to the quantum Singleton bound. Compared to Reed-Solomon codes, Hermitian codes admit comparable lengths over smaller alphabets, enabling more efficient implementations.